Yes, this etymology gives many miminismes, but I liked the detail of the minium, used to make red ink. The dispute, it seems, started from 1714. I looked it up and could not find anything in English. This transl. text says:
For this ink the 'rubricator' used pulverized red minium, hence the name 'miniature'.

It was used mainly for rubrics - in early books and manuscripts, a title, initial letter, or the like lettered in red or in some other distinctive fashion.

As could be expected the word rubric connects with 'red' as well.
rubric:
c.1375, "directions in religious services" (often in red writing), from O.Fr. rubrique, from L. rubrica "red ochre, red coloring matter," from ruber, from PIE base *rudhro- (see red).